Problem: Solve for $x$ and $y$ using substitution. ${3x-6y = 12}$ ${y = 2x-11}$
Since $y$ has already been solved for, substitute $2x-11$ for $y$ in the first equation. ${3x - 6}{(2x-11)}{= 12}$ Simplify and solve for $x$ $3x-12x + 66 = 12$ $-9x+66 = 12$ $-9x+66{-66} = 12{-66}$ $-9x = -54$ $\dfrac{-9x}{{-9}} = \dfrac{-54}{{-9}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {y = 2x-11}\thinspace$ to find $y$ ${y = 2}{(6)}{ - 11}$ $y = 12 - 11$ $y = 1$ You can also plug ${x = 6}$ into $\thinspace {3x-6y = 12}\thinspace$ and get the same answer for $y$ : ${3}{(6)}{ - 6y = 12}$ ${y = 1}$